The area bounded by the curves y² = 4x and x² = 4y is:
The area bounded by the curves y² = 4x and x² = 4y is:
- A. 16/3 sq units
- B. 8/3 sq units
- C. 4/3 sq units
- D. 32/3 sq units
Answer: A) 16/3 sq units
Explanation: Solving: (x²/4)² = 4x → x⁴/16 = 4x → x⁴ = 64x → x(x³ − 64) = 0 → x = 0, 4. Area = ∫[0 to 4] (√(4x) − x²/4) dx = [4√x × (2/3)x^(1/2) − x³/12]₀⁴ = (8/3)×4^(3/2) − 64/12 = (8/3)×8 − 16/3 = 64/3 − 16/3 = 48/3 = 16/3 sq units.
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